Related papers: Mean first-passage time of quantum transition proc…
Often sharp changes in cellular behavior are triggered by thresholded events, i.e., by the attainment of a threshold value of a relevant cellular or molecular dynamical variable. Since the governing variable itself typically undergoes noisy…
We present an analytical approximation scheme for the first passage time distribution on a finite interval of a random walker on a random forcing energy landscape. The approximation scheme captures the behavior of the distribution over all…
The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact…
We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the…
The quantum Fourier transform (QFT) is a key primitive for quantum computing that is typically used as a subroutine within a larger computation, for instance for phase estimation. As such, we may have little control over the state that is…
We discuss experimental situations that consist of multiple preparation and measurement stages. This leads us to a new approach to quantum mechanics. In particular, we introduce the idea of multi-time quantum states which are the…
We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential $v(x)$ in a finite domain. We focus on the cases in which the external potential is confining, of the…
The first-passage time (FPT) of a stochastic signal to a threshold is a fundamental observable across physics, biology, and finance. While renewal shot noise is a canonical model for such signals, analytical results for its FPT have…
Martensites are long-lived nonequilibrium structures produced following a quench across a solid state structural transition. In a recent paper (Phys. Rev. Lett. 78, 2168 (1997)), we had described a mode-coupling theory for the morphology…
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of…
We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world…
Despite the fact that a complete theoretical description of critical phenomena in connection with phase transitions has been well-established through the renormalization group theory, the microscopic nature of the phase transitions remains…
We study analytically and numerically the mean fastest first-passage time (fFPT) to an immobile target for an ensemble of $N$ independent finite-speed random searchers driven by dichotomous noise and described by the telegrapher's equation.…
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected…
With nontrivial entropy production, first passage process is one of the most common nonequilibrium process in stochastic thermodynamics. Using one dimensional birth and death precess as a model framework, approximated expressions of mean…
Quantum phase transitions occur at zero temperature when some non-thermal control-parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a…
We put forward a novel approach to study the evolution of an arbitrary open quantum system under a resetting process. Using the framework of renewal equations, we find a universal behavior for the mean first return time that goes beyond…
Generic quantum systems --as much as their classical counterparts-- pass arbitrarily close to their initial state after sufficiently long time. Here we provide an essentially exact computation of such recurrence times for generic…
These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the…
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The…